Make sure you write the terms left to right from highest degree to lowest degree for both the dividend and the divisor.
The long division process goes as follows: Imagine taking just the highest degree term from the dividend in our example, x2 and dividing it by the highest degree term of the divisor in our example, x. The result is the first term of our "quotient". In our example, the result will be x.
Usually, you should write the answer above the term of the same degree as the result:. Write this result below the dividend, making sure you line up each term of the result under the term in the dividend with the same degree:.
One way to do this without losing track of signs is to reverse all the signs of the terms of our result and add like terms:. Note that the first term will always cancel out and possibly others will as well. Now, we repeat the process of long division, taking the highest degree of our new polynomial which is 2x and dividing it by the highest degree term of the divisor again, x ; the result is 2. That is our second term of our quotient, and we write it as follows:. We stop once we have no more terms to bring down.
The result from the last step is the remainder. Next decide what we need to multiply x 2 by to get x 4. We repeat this process until the degree of the remainder is less than the degree of the denominator. I designed this web site and wrote all the lessons, formulas and calculators. If you want to contact me, probably have some question write me using the contact form or email me on.
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Monomials can be multiplied and divided like any other algebraic expression. They can be simplified if the bases are the same using the rules of exponents.
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